Avalanche multiplication properties of GaAs calculated from spatially transient ionisation coefficients

In this paper the high field phenomenon of avalanche multiplication in a GaAs p-i-n infrared detector is studied using a Monte-Carlo simulation. The Lucky-Drift model of impact ionization is used to give the characteristic lengths for transport through the device. The transport is then modelled by generating motion consistent with the probability functions derived from the mean free paths. This produces a spatially transient ionization coefficient for each carrier and allows the realistic statistical simulation of avalanche multiplication. Properties such as mean gain, multiplication noise and the transient response to a photonic pulse have been calculated and explained for a length of i-GaAs, with an emphasis on short active region phenomena. The effect on the ionization coefficients of a periodic field change has been investigated. It has been found that the effective carrier deadspace is approx. 1.35 times the absolute deadspace. The transient current calculations indicate the narrow bandwidth of this type of device. The presence of a periodic field change, caused by periodic δ-doping, was found to increase both electron and hole ionization coefficients by different proportions.     

Effect of dead space on gain and noise in Si and GaAs avalanchephotodiodes

The effect of dead space on the mean gain, the excess noise factor, and the avalanche breakdown voltage for Si and GaAs avalanche photodiodes (APDs) with nonuniform carrier ionization coefficients are examined. The dead space, which is a function of the electric field and position within the multiplication region of the APD, is the minimum distance that a newly generated carrier must travel in order to acquire sufficient energy to become capable of causing impact ionization. Recurrence relations in the form of coupled linear integral equations are derived to characterize the underlying avalanche multiplication process. Numerical solutions to the integral equations are obtained and the mean gain and the excess noise factor are computed     

Excess noise analysis of separate absorption multiplication regionsuperlattice avalanche photodiodes

The operation of a separate absorption multiplication region avalanche photodiode (SAM-APD) introduces noise as results of randomness in the number and in the position at which dark carrier pairs are generated, randomness in the photon arrival number, randomness in the carrier multiplication, and the number and the position of the photogenerated carriers in the bulk of the diode. The dark current results in a smaller mean multiplication gain in excess noise factor versus mean multiplication plot due to the partial multiplication process of these generated carriers compared to the usual values associated with carriers injected at one edge of the diode. Previous analyses of mean multiplication and excess noise factor for an arbitrary superposition of injected carriers are extended to allow the presence of dark carriers in the multiplication region under the model, which admits variation (with position) of the band-gap, dark generated rate, and ionization coefficients with each stage for the superlattice APD, and the presence of impact ionization in the absorption region. The calculations reveal the presence of impact ionization carriers in the absorption region which results in a larger excess noise factor than the usual values associated with carriers injected at one edge of the device, and fits well with experimental results     

A stochastic invariant imbedding approach to avalanche noise in semiconductors

The multiplication statistics in an avalanche region in semiconductors by impact ionization are treated stochasticly by means of the invariant imbedding technique. An explicit result is obtained for the variance of the process for arbitrary ionization coefficients. A simple formula is derived for the determination of the spectral density of the fluctuations, caused by multiplication statistics. Formulae will be given for the mean and the variance of both electrons and holes. An exact result is obtained for a linear spatial dependency of the ionization coefficients.     

Mean gain of avalanche photodiodes in a dead space model

Based on a first order expansion of the recursive equations, we derive approximate analytical expressions for the mean gain of avalanche photodiodes accounting for dead space effects. The analytical solutions are similar to the popular formula first obtained in local approximation, provided that the ionization coefficients, α and β, are replaced with suitable effective ionization coefficients depending on dead space. The approximate solutions are in good agreement with the exact numerical solutions of the recursive equations for p-i-n devices as well as for photodiodes with nonconstant electric field profile. We also show that dead space causes non negligible differences between the values of the effective ionization coefficients entering in carrier continuity equations, the carrier ionization probability per unit length and the ionization coefficients derived by experimenters from multiplication measurements     

The frequency response of avalanching photodiodes

The Townsend equations for avalanche breakdown in back biased p-n junctions may be derived from the transport equations for semiconductors. Integral solutions of the time independent equations are well known. An integral solution of the time dependent equations is given for multiplication by one carrier only. An exact solution is given for multiplication by two carriers with equal ionization coefficients in a constant junction field. The Townsend equations are nonlinear because of space charge effects. It is shown, however, that the nonlinearity, which imposes an upper limit on the current multiplication possible, is not important until the total multiplied current approaches the space charge limited current for the junction. Assuming multiplication is due to one carrier, frequency response curves are calculated for constant and linear junction fields and for a generation rate, due to photon absorption, which is either uniform or given by a delta function at the junction boundary. The curves indicate a relatively slight dependence of the frequency response on multiplication. Frequency response curves are also given for multiplication by both carriers with equal ionization coefficients when the junction field is constant. In this case the frequency response decreases continuously as the multiplication is increased. For multiplication by two carriers with unequal ionization coefficients, the frequency response is independent of multiplication until the product of the multiplication and the ratio of the ionization coefficients approaches one. Thereafter the frequency response decreases with multiplication.     

Simplified particle simulation of millimeter-wave IMPATT devices

A simplified microscopic model for investigating energy relaxation effects in millimeter-wave IMPATT devices is presented. A statistical process is used to describe electron-hole multiplication by impact ionization from knowledge of the ionization coefficients. These coefficients are assumed to be functions of the individual energy of carriers (holes and electrons). A relaxation time formulation is used to calculate the energy of each carrier. Drift in the electric field and diffusion are modeled using the diffusive model proposed by Hockney. Simulations are carried out for silicon diodes. It is found that inclusion of the energy relaxation mechanisms modifies mainly the avalanche process for such material. The implications of these mechanisms on device performances are then discussed by calculating the large signal level dependence of the conversion efficiency and admittance for a typical double-drift structure at 100 GHz. The resulting calculations show good agreement with existing experimental data on these structures.     

Dead-space-based theory correctly predicts excess noise factor forthin GaAs and AlGaAs avalanche photodiodes

The conventional McIntyre carrier multiplication theory for avalanche photodiodes (APDs) does not adequately describe the experimental results obtained from APDs with thin multiplication-regions. Using published data for thin GaAs and Al_0.2Ga_0.8As APDs, collected from multiplication-regions of different widths, we show that incorporating dead-space in the model resolves the discrepancy. The ionization coefficients of enabled carriers that have traveled the dead space are determined as functions of the electric field, within the confines of a single exponential model for each device, independent of multiplication-region width. The model parameters are determined directly from experimental data. The use of these physically based ionization coefficients in the dead-space multiplication theory, developed earlier by Hayat et al. provide excess noise factor versus mean gain curves that accord very closely with those measured for each device, regardless of multiplication-region width. It is verified that the ratio of the dead-space to the multiplication-region width increases, for a fixed mean gain, as the width is reduced. This behavior, too, is in accord with the reduction of the excess noise factor predicted by the dead-space multiplication theory     

Effect of dead space on the excess noise factor and time responseof avalanche photodiodes

The effect of dead space on the statistics of the gain process in continuous-multiplication avalanche photodiodes (APDs) is determined using the theory of age-dependent branching processes. The dead space is the minimum distance that a newly generated carrier must travel in order to acquire sufficient energy to cause an impact ionization. Analytical expressions are derived for the mean gain, the excess noise factor, and the mean and standard deviation of the impulse response function, for the dead-space-modified avalanche photodiode (DAPD), under conditions of single carrier multiplication. The results differ considerably from the well-known formulas derived by R.J. McIntyre and S.D. Personick in the absence of dead space. Relatively simple asymptotic expressions for the mean gain and excess noise factor are obtained for devices with long multiplication regions. In terms of the signal-to-noise ratio (SNR) of an optical receiver in the presence of circuit noise, it is established that there is a salutory effect of using a properly designed DAPD in place of a conventional APD. The relative merits of using DAPD versus a multilayer (superlattice) avalanche photodiode (SAPD) are examined in the context of receiver SNR; the best choice turns out to depend on which device parameters are used for the comparison     

Theory of a new three-terminal microwave power amplifier

The feasibility of a new three-terminal linear power amplifier has been demonstrated both theoretically and experimentally from 0.5 to 3.0 GHz. The new amplifier is similar to an n-p-n bipolar transistor in configuration but develops extra power gain through avalanche multiplication and by the use of transit time in the collector. Major differences in the construction of the two devices are in their collector doping profiles and depletion layer widths. It is estimated that this new amplifier will be capable of several watts of power output at 10 GHz with useful gain, good linearity, and wide dynamic range. An acronym, CATT, which stands for controlled avalanche transit-time triode, is used to designate this new microwave semiconductor device. In this paper, the theory of the CATT is developed. It is found to be dc and RF stable. The necessary conditions on the ionization coefficients for signal amplification are investigated. The emitter-base dynamics of the CATT are shown to be quite different from a transistor due to hole feedback from the avalanche multiplication region. This phenomena results in a more uniform emitter current injection and better use of the emitter finger area than for transistors.     

Avalanche Noise Characteristics in Submicron InP Diodes

We report excess noise factors measured on a series of InP diodes with varying avalanche region thickness, covering a wide electric field range from 180 to 850 kV/cm. The increased significance of dead space in diodes with thin avalanche region thickness decreases the excess noise. An excess noise factor of F = 3.5 at multiplication factor M = 10 was measured, the lowest value reported so far for InP. The electric field dependence of impact ionization coefficients and threshold energies in InP have been determined using a non-local model to take into account the dead space effects. This work suggests that further optimization of InP separate absorption multiplication avalanche photodiodes (SAM APDs) could result in a noise performance comparable to InAlAs SAM APDs.     

Simulation of avalanche multiplication of electrons in photodetectors with blocked hopping conduction

The avalanche electron multiplication in a silicon structure with blocked hopping conduction is simulated for the photon-counting mode. The acceleration of an electron in an electric field that is linearly dependent on the coordinate, the elastic scattering of electrons by longitudinal acoustic phonons, the inelastic scattering of electrons by intervalley phonons, and the ionization of impurity centers are taken into account when considering the motion of an electron. A simple algorithm making it possible to calculate directly the coordinates of all ionized centers in an avalanche and the probability of N electrons leaving the avalanche if a single electron has entered the multiplication region is suggested. It is shown that this probability is at its maximum in the vicinity of 〈N〉 (the mean value of the leaving-probability function), which is consistent with experimental data.     

An analytical approach to study the effect of carrier velocities onthe gain and breakdown voltage of avalanche photodiodes

A simplified model for calculating gain and breakdown voltage of avalanche photodiodes (APDs) having constant ionization coefficients in their multiplication layer is presented. Good agreement is seen between the calculated results and the experimental data for published InP-InGaAs separate absorption, grading, charge, and multiplication (SAGCM) APDs. The model denotes that the gain and the breakdown voltage have a dependence on the carrier velocity ratio that is not predicted by conventional models. Hence, by comparing the calculated and measured static characteristics of the APD, one can estimate the velocity of minority carriers in the multiplication region of the device     

Impact ionization characteristics of III-V semiconductors for awide range of multiplication region thicknesses

Recently, an impact ionization model, which takes the nonlocal nature of the impact ionization process into account, has been described. This model incorporates history-dependent ionization coefficients. Excellent fits to experimental gain and noise measurements for GaAs were achieved using an effective field approach and simple analytical expressions for the ionization probabilities. In the paper, we briefly review the history-dependent model and apply it to Al_0.2 Ga_0.8As, In_0.52Al_0.48As and InP avalanche photodiodes. For the study, the gain and noise characteristics of a series of homojunction avalanche photodiodes with different multiplication thicknesses were measured and fit with the history-dependent model. A “size-effect” in thin (<0.5 μm) multiplication regions, which is not adequately characterized by the local-field avalanche theory, was observed for each of these materials. The history-dependent model, on the other hand, achieved close agreement with the experimental results     

A new look at impact ionization-Part I: A theory of gain, noise,breakdown probability, and frequency response

Impact ionization in thick multiplication regions is adequately described by models in which the ionization coefficients are functions only of the local electric field. In devices with thin multiplication lengths, nonlocal effects become significant, necessitating new models that account for the path that a carrier travels before gaining sufficient energy to impact ionize. This paper presents a new theory that incorporates history-dependent ionization coefficients, and it is shown that this model can be utilized to calculate the low-frequency properties of avalanche photodiodes (APD's) (gain, noise, and breakdown probability in the Geiger mode) and the frequency response. A conclusion of this work is that an ionization coefficient is not a fundamental material characteristic at a specific electric field and that any experimental determination of ionization coefficients is valid only for the particular structure on which the measurement was performed     

RF linearity characteristics of SiGe HBTs

Two-tone intermodulation in ultrahigh vacuum/chemical vapor deposition SiGe heterojunction bipolar transistors (HBTs) were analyzed using a Volterra-series-based approach that completely distinguishes individual nonlinearities. Avalanche multiplication and collector-base (CB) capacitance were shown to be the dominant nonlinearities in a single-stage common emitter amplifier. At a given I_c an optimum V_ce exists for a maximum third-order intercept point (IIP3). The IIP3 is limited by the avalanche multiplication nonlinearity at low I_c, and limited by the C_CB nonlinearity at high I_c. The decrease of the avalanche multiplication rate at high I_c is beneficial to linearity in SiGe HBTs. The IIP3 is sensitive to the biasing condition because of strong dependence of the avalanche multiplication current and CB capacitance on I_c and V_ce. The load dependence of linearity was attributed to the feedback through the CB capacitance and the avalanche multiplication in the CB junction. Implications on the optimization of the transistor biasing condition and transistor structure for improved linearity are also discussed     

Gain-bandwidth characteristics of thin avalanche photodiodes

The frequency-response characteristics of avalanche photodiodes (APDs) with thin multiplication layers are investigated by means of a recurrence technique that incorporates the history dependence of ionization coefficients. In addition, to characterize the autocorrelation function of the impulse response, new recurrence equations are derived and solved using a parallel computer. The mean frequency response and the gain-bandwidth product are computed and a simple model for the dependence of the gain-bandwidth product on the multiplication-layer width is set forth for GaAs, InP, Al_0.2Ga_0.8As, and In_0.52Al_0.48 As APDs. It is shown that the dead-space effect leads to a reduction (up to 30%) in the bandwidth from that predicted by the conventional multiplication theory. Notably, calculation of the power-spectral density of the photocurrent reveals that the presence of dead space also results in a reduction in the fluctuations in the frequency response. This result is the spectral generalization of the reduction in the excess noise factor in thin APDs and reveals an added advantage of using thin APDs in ultrafast receivers     

Impact-ionization and noise characteristics of thin III-V avalanchephotodiodes

It is, by now, well known that McIntyre's localized carrier-multiplication theory cannot explain the suppression of excess noise factor observed in avalanche photodiodes (APDs) that make use of thin multiplication regions. We demonstrate that a carrier multiplication model that incorporates the effects of dead space, as developed earlier by Hayat et al. provides excellent agreement with the impact-ionization and noise characteristics of thin InP, In_0.52 Al_0.48As, GaAs, and Al_0.2Ga_0.8As APDs, with multiplication regions of different widths. We outline a general technique that facilitates the calculation of ionization coefficients for carriers that have traveled a distance exceeding the dead space (enabled carriers), directly from experimental excess-noise-factor data. These coefficients depend on the electric field in exponential fashion and are independent of multiplication width, as expected on physical grounds. The procedure for obtaining the ionization coefficients is used in conjunction with the dead-space-multiplication theory (DSMT) to predict excess noise factor versus mean-gain curves that are in excellent accord with experimental data for thin III-V APDs, for all multiplication-region widths     

Frequency response theory for multilayer photodiodes

An exact solution is developed for the frequency response of photodiodes composed of multiple spatially uniform layers. Each layer is analyzed separately to obtain a set of linear response coefficients. The response of the multilayer diodes is calculated using matrix algebra. Effects of carrier transit, electron and hole trapping, avalanche decay, and finite absorption length are included in the analysis. The results of R.B. Emmons (1967) and G. Lucovsky et al. (1958) for avalanche photodiodes (APDs) and p-i-n's, respectively, are obtained as special cases. The theory is illustrated by applying it to the separated absorption and multiplication     

An analytical approximation for the excess noise factor ofavalanche photodiodes with dead space

Approximate analytical expressions are derived for the mean gain and the excess noise factor of avalanche photodiodes including the effect of dead space. The analysis is based on undertaking a characteristic-equation approach to obtain an approximate analytical solution to the existing system of recurrence equations which characterize the statistics of the random multiplication gain. The analytical expressions for the excess noise factor and the mean gain are shown to be in good agreement with the exact results obtained from numerical solutions of the recurrence equations for values of the dead space reaching up to 20% of the width of the multiplication region